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The MOSDEF Survey: Dissecting the star-formation rate vs. stellar mass relation using H$α$ and H$β$ emission lines at z ~ 2

We present results on the star-formation rate (SFR) versus stellar mass ($M_*$) relation (i.e., the "main sequence") among star-forming galaxies at 1.37$\leq$$z$$\leq$2.61 using the MOSFIRE Deep Evolution Field (MOSDEF) survey. Based on a sample of 261 galaxies with H$α$ and H$β$ spectroscopy, we have estimated robust dust-corrected instantaneous SFRs over a large range in $M_*$ ($\sim10^{9.5}-10^{11.5}M_\odot$). We find a correlation between log(SFR(H$α$)) and log($M_*$) with a slope of 0.65$\pm$0.08 (0.58$\pm$0.10) at 1.4<z<2.6 (2.1<z<2.6). We find that different assumptions for the dust correction, such as using the color-excess of the stellar continuum to correct the nebular lines, sample selection biases against red star-forming galaxies, and not accounting for Balmer absorption can yield steeper slopes of the log(SFR)-log($M_*$) relation. Our sample is immune from these biases as it is rest-frame optically selected, H$α$ and H$β$ are corrected for Balmer absorption, and the H$α$ luminosity is dust-corrected using the nebular color-excess computed from the Balmer decrement. The scatter of the log(SFR(H$α$))-log($M_*$) relation, after accounting for the measurement uncertainties, is 0.31 dex at 2.1<z<2.6, which is 0.05 dex larger than the scatter in log(SFR(UV))-log($M_*$). Based on comparisons to a simulated SFR-$M_*$ relation with some intrinsic scatter, we argue that in the absence of direct measurements of galaxy-to-galaxy variations in the attenuation/extinction curves and the IMF, one cannot use the difference in the scatter of the SFR(H$α$)- and SFR(UV)-$M_*$ relations to constrain the stochasticity of star formation in high-redshift galaxies.